Spatially modulated kinks in shallow granular layers

Abstract

We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.

Relevance of system size to the steady-state properties of tapped granular systems

“…Since φ and are inhomogeneous in the vertical direction due to gravity, using a layer warrants that we focus on a region where a few macroscopic variables can describe the macrostate without the presence of significant spatial variations of the mean φ and in the region. Additionally, the free surface of the column of grains is not horizontal in general, especially for wide cells as described by others [4,9,24,25] (see also Fig. 2).…”

Internal noise and system size effects induce nondiffusive kink dynamics

“…Interfaces between these metastable states appear in the form of propagating fronts and give rise to rich spatiotemporal dynamics [5][6][7]. Front dynamics occurs in systems as different as walls separating magnetic domains [8], directed solidification processes [9], nonlinear optical systems [10,11,13,33], oscillating chemical reactions [14], fluidized granular media [15][16][17][18][19][20][21], and population dynamics [22][23][24], to mention a few. From the point of view of dynamical systems theory, in one spatial dimension a front is a nonlinear solution that is identified in the comoving frame system as a heteroclinic orbit linking two spatially extended uniform states [25,26].…”

“…Recently in Refs. [20,21], observations of kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow were reported each domain varied periodically with half of the forcing period. Figure 1 shows a granular kink observed at a given moment and the respective dynamic evolution of the kink position.…”

Discrete and continuum descriptions of shaken granular matter

“…It is known that fluctuations in macroscopic fields are proportional to the number of particles involved in the system, and thus the difference of noise intensity between molecular and granular systems is expected to be enormous. For example, only by including additive noise terms to the appropriate universal amplitude equations it has been possible to follow the growth and saturation of the relevant modes in pattern formation scenarios [34,35]. It then becomes possible to establish an analogy with systems with the same amplitude equations, sometimes for quite different physical phenomena [36,37].…”

“…The low number of constituents of granular media, when compared to molecular fluids, provides a unique way of studying the role of noise in phase transitions [33,34,35]. It is known that fluctuations in macroscopic fields are proportional to the number of particles involved in the system, and thus the difference of noise intensity between molecular and granular systems is expected to be enormous.…”